RC Slab Analysis and Design
| Span Strip | Location | Moment $M_u$ (kN·m) | Req. $\rho$ (%) | Req. $A_s$ (mm²) | Provided Rebar | Prov. $A_s$ (mm²) |
|---|---|---|---|---|---|---|
| Short Span (X) | + Midspan (Bottom) | 0.0 | 0.00 | 0 | - | 0 |
| - Support (Top) | 0.0 | 0.00 | 0 | - | 0 | |
| Long Span (Y) | + Midspan (Bottom) | 0.0 | 0.00 | 0 | - | 0 |
| - Support (Top) | 0.0 | 0.00 | 0 | - | 0 |
| Item Description | Quantity | Unit | Remarks |
|---|---|---|---|
| Concrete Volume | 0.0 | m³ | L_x × L_y × h |
| Formwork Area | 0.0 | m² | Soffit + 4 Edges |
| Rebar Weight (Short Span X) | 0 | kg | Main + Top Support Steel |
| Rebar Weight (Long Span Y) | 0 | kg | Secondary + Top Support Steel |
| Total Rebar Weight | 0 | kg | Ratio: 0.0 kg/m³ |
The tool automatically generates the ultimate factored load ($w_u$) by evaluating all standard load combinations required by the selected design code and explicitly picking the maximum governing case.
Based on the aspect ratio $m = L_y / L_x$.
- If $m > 2$: The slab is One-Way. Bending occurs almost exclusively in the short direction. The long direction only requires shrinkage/temperature steel.
- If $m \le 2$: The slab is Two-Way. The tool distributes $w_u$ to the X and Y continuous strips using Grashof-Rankine theory: $W_x = w_u \frac{L_y^4}{L_x^4 + L_y^4}$.
Once the load is distributed to the 1D strips, the tool calculates the precise Shear Force ($V$) and Bending Moment ($M$) profiles based on the user-defined edge supports.
Edges rest on supports but are free to rotate. Creates purely positive moment (tension at bottom), requiring only bottom reinforcement.
Edges are cast monolithically with stiff supports, preventing rotation. Generates high negative moments at supports (requiring top rebar) and reduces midspan positive moment.
One edge is free to rotate (e.g., resting on a masonry wall) while the other is fully fixed. Creates an asymmetrical bending profile.
The required reinforcement area is calculated based on the selected structural code to provide the necessary nominal moment capacity.
In continuous or fixed slabs, negative bending moments ($-M$) peak at the supports and transition to positive moments ($+M$) near the midspan. The point where the moment crosses zero is called the point of contraflexure.
Because the center of the slab experiences no negative moment, top reinforcement is not structurally required across the entire span. Standard detailing practice (e.g., ACI 315) dictates that top bars be curtailed (cut off) past the point of contraflexure—typically extending approximately $0.30L$ to $0.33L$ from the face of the support into the span. This safely resists support tension forces while significantly reducing material costs.
| Occupancy / Use | Metric (kPa) | Imp (psf) |
|---|---|---|
| Residential / Hotel Rooms | 2.0 | 40 |
| Offices | 2.5 | 50 |
| Classrooms | 3.0 | 60 |
| Corridors (Above 1st Flr) | 4.0 | 80 |
| Retail / Assembly Areas | 4.8 | 100 |
| Heavy Storage / Library | 6.0+ | 125+ |
| Exposure Condition | Metric (mm) | Imp (in) |
|---|---|---|
| Slabs/Walls (Dry) | 20 | 0.75 |
| Beams/Cols (Internal) | 40 | 1.5 |
| Weather Exposed | 40 - 50 | 1.5 - 2.0 |
| Cast Against Earth | 75 | 3.0 |
| Material | Metric (MPa) | Imp (psi) |
|---|---|---|
| Concrete (Standard) | 21, 25, 28 | 3000, 4000 |
| Concrete (High Strength) | 35, 40, 50 | 5000, 6000 |
| Steel Rebar (Grade 40) | 280 | 40,000 |
| Steel Rebar (Grade 60) | 420 | 60,000 |
| Steel Rebar (B500B/Gr 75) | 500 | 75,000 |
| Support Condition | 1-Way |
|---|---|
| Simply Supported | $L / 20$ |
| One End Cont. | $L / 24$ |
| Both Ends Cont. | $L / 28$ |
| Cantilever | $L / 10$ |
| Two-Way (No Beams) | Ratio |
|---|---|
| Flat Plate (Exterior) | $L_n / 30$ |
| Flat Plate (Interior) | $L_n / 33$ |
| Flat Slab (Exterior) | $L_n / 33$ |
| Flat Slab (Interior) | $L_n / 36$ |
* ACI 318 baseline for $f_y = 420$ MPa (60 ksi). For other yield strengths, multiply One-Way $h$ by $(0.4 + f_y / 700)$. $L_n$ is clear span. Flat Plate = No drop panels. Flat Slab = With drop panels.
Rebar Spacing Limits (Slabs)- Max Spacing: Generally the smaller of $3h$ or $450\text{mm}$ (18").
- Min Spacing: To allow aggregate passing, generally $> 25\text{mm}$ (1") or $1.33 \times$ max aggregate size.
- ACI 318: Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute.
- EN 1992-1-1 (Eurocode 2): Design of concrete structures - Part 1-1: General rules and rules for buildings. European Committee for Standardization.
- IS 456: Plain and Reinforced Concrete - Code of Practice. Bureau of Indian Standards.
- BS 8110-1: Structural use of concrete. Code of practice for design and construction. British Standards Institution.
- GB 50010: Code for design of concrete structures. Ministry of Housing and Urban-Rural Development of the PRC.
- JSCE: Standard Specifications for Concrete Structures - Design. Japan Society of Civil Engineers.
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